Fly is a very useful HM that can be learned by Flying-type Pokémon. It can take you to and from cities a lot faster than walking.

Steps

1

Make sure you have defeated Lt.Surge[1], the gym leader who specializes in Electric-type Pokémon, in order to use the HM Fly once you have gotten it. Your Pokémon will not listen to you if you try making it use Fly when you don't have the Thunder Badge (your reward for defeating Lt. Surge).

2

Make sure you have a Pokémon that knows Cut. You can only use Cut if you have defeated Misty (Cerulean City gym leader) and received the Cascade Badge.

3

(Optional) Have a Pokémon to teach Fly to. Almost all Flying-type Pokémon can learn Fly.

4

Go to Celadon City.

5

Leave Celadon City through the west exit.

6

Cut the tree above you and go through the gap.

7

Follow the path that goes through the top half of the guard house until you reach a house.